[hist-analytic] Quine, Aune, Jones: on defining analyticity

Baynesr at comcast.net Baynesr at comcast.net
Sat Mar 21 13:42:20 EDT 2009


Roger, 

On analyticity, post Kant, prior to 
Carnap, the idea is kicked around 
in terms of validity, in particular 
proof theory. I know of no definition 
of 'analytic' which is not language 
specific, post Tarski. Can you cite 
one? If this is 
your view, and you may be right, I think 
what we need is something to justify this, 
beginning with what you take 'analytic' 
to mean. Indeed, my reason for having 
some sympathy for what I take to be 
your program is that neither truth 
nor validity captures analyticity. 
There is this business about "essence" 
that will not go away, unless we make 
the Quinean (Carnapian) "semantic 
ascent." 

>I do of course accept that when analyticity 
>is defined explicitly in terms of meanings, 
>or when that it done indirectly as in my 
>proposed definition, then to apply the notion 
>to specific languages you need to have some 
>information about the semantics of the 
>languages in question. 

Yes. However, meaning is language specific, 
like 'analytic' in my opinion. A set of 
morphemes may have one meaning in one language 
and another in another language. 


>So far as Kant is concerned, my proposal is 
>intentionally divergent from Kant. 
>My monograph is to make a feature of 
>Hume's fork, which Kant was inspired to reject. 

Since I'm, more or less, a Kantian, it is 
essential to any comment on my part that you 
flesh this out or be more specific. 


>Well they don't use the terminology, but one 
>can see in mathematical practice that 
>mathematicians take great pains to ensure 
>that mathematics is analytic. 

There are mathematicians of great talent 
who affirm the Kantian position, e.g. 
Poincare. 


>I'm afraid I don't understand your point here. 

The example I've seen most often is: 

(Ex)(Ey)(z)[f(x) & f(y) -> f(z)]. 

In a universe where the domain is 2 or 
less, it is logical truth. But in a 
universe of 3 individuals it is not. 

>All theorems of sound deductive systems 
>are analytic in the sense in which Carnap 
>and I use the term, and in the sense 
>"true in virtue of meaning". 

Well, I'm still not sure, since Carnap 
offers several definitions of 'analytic'. 
Do you have one in mind in particular? 
Which? 

>>By the way, I can't find your remark on Kripke 
>>on the underdermination of truth. 

>Doesn't ring any bells for me, are you sure 
>it was my remark? 

I'm sure it was you. Let me look for it. It 
was very good, as I recall. Let me look. 

Regards 

STeve 
----- Original Message ----- 
From: "Roger Bishop Jones" <rbj at rbjones.com> 
To: hist-analytic at simplelists.com 
Sent: Friday, March 20, 2009 5:12:59 PM GMT -05:00 US/Canada Eastern 
Subject: Re: Quine, Aune, Jones: on defining analyticity 

On Thursday 19 March 2009 11:34:38 steve bayne wrote: 
... 
>In order to assess your theory of analyticity, 
>we need to know what "objects" can be said to 
>be analytic on your account. 

I didn't really put forward a "theory", 
I put forward a definition, which was intended 
to be read as a proposal for usage, not a 
description or explication of previous usage 
(though it is arguably consistent with much 
prior usage). 

>On Quine, you are incorrect, in my opinion. 
>Quine is not calling for a general notion to 
>be explained; he is denying the existence of 
>any general notion. I doubt that the idea 
>of such a general notion would make sense to 
>him. Same with 'true'. 

The two are not incompatible. 
He says that before we can understand rules 
for specific languages we "must" understand 
the general notion. 
He is calling for the general notion to be 
explained, and denying that it can be. 

Prior to Carnap, so far as I am aware, 
no-one discussed anything but the general 
notion (though not explicitly talking in 
terms of variable L). 
I believe it to be a mistake ever to 
consider language specific definitions 
of analyticity. 

>Now if you take analyticity as truth based 
>on meaning, then you have 'meaning' to 
>contend with; you need to establish what 
>meaning is and, especially, if you are 
>asserting a connection between meanings etc. 
>Keep in mind that 'meanings', even, if you 
>accept translation are creatures or language; 
>so if you want to arrive at, say, a Kantian 
>idea of analyticity you need to link meanings 
>and concepts. Fregean functions are 
>sometimes thought to serve this purpose; then 
>there is the notion of meanings as captured 
>in "worlds"; that is, senses, intensions 
>etc. become expressed in terms of extensions 
>over worlds (essentially Carnap, Montague). 

I do of course accept that when analyticity 
is defined explicitly in terms of meanings, 
or when that it done indirectly as in my 
proposed definition, then to apply the notion 
to specific languages you need to have some 
information about the semantics of the 
languages in question. 

I would not look back to Frege for help 
in dealing with semantics these days, though 
no doubt his work has contributed in important 
ways to modern methods in this area. 

So far as Kant is concerned, my proposal is 
intentionally divergent from Kant. 
My monograph is to make a feature of 
Hume's fork, which Kant was inspired to reject. 

>One, among several, complications related to 
>analyticity is related to mathematical foundations. 
>This is not an epistemological area of investigations. 
>Validity theory is not designed to solve the 
>problem of skepticism in mathematics. Recall my 
>question about whether truths of logic, even 
>of the Boolean sort, are analytic? Quine and 
>others take this as given. I don't. 

Well they don't use the terminology, but one 
can see in mathematical practice that 
mathematicians take great pains to ensure 
that mathematics is analytic. 

(i.e. they would not accept a proof of some 
result as of any value if they were not 
satisfied that the deductive system was sound) 

>At the level 
>of functional logic we find ourselves in 
>deeper waters - confusion over problems of 
>infinite cardinals, for example. But what is 
>very puzzling is the role of domain size in 
>axiomatic treatments of foundations. whether 
>a truth in functional logic (first order) is 
>a tautology or simply false depends on the 
>size of the universe. 

I'm afraid I don't understand your point here. 

>The old Axiom of Infinity 
>was indicative of this problem. If the size of 
>a domain is contingent then it is arguable that 
>no truth of logic is analytic in a certain sense. 

All theorems of sound deductive systems 
are analytic in the sense in which Carnap 
and I use the term, and in the sense 
"true in virtue of meaning". 

>Now a lot of people will take exception to this 
>but I've never had a satisfactory answer. 

If I understood the question I would have a 
shot at giving you satisfaction. 

>By the way, I can't find your remark on Kripke 
>on the underdermination of truth. 

Doesn't ring any bells for me, are you sure 
it was my remark? 

Roger 
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